2.3.7 Thermal conductivities

Definition and units

The thermal conductivity, λ, of a substance may
be defined as the quantity of heat transmitted, Q, due to unit
temperature gradient, in unit time under steady conditions in a direction
normal to a surface of unit area, when the heat transfer is dependent only on
the temperature gradient.

λ =
− Q

∂T

∂n

In this section thermal conductivity
values are assembled for metallic, semi-conducting and insulating elements,
representative groups of alloys, refractories and miscellaneous constructional
and insulating materials, some liquids and some gases. The values are expressed
in the SI unit W m−1 K−1 throughout. Factors
for converting to other units are as follows:

1 W m−1 K−1
= 0.01 J cm cm−2
s−1 K−1

=
0.002 388 cal cm cm−2 s−1
K−1

=
0.859 8 kcal m m−2 h−1
K−1

=
0.001 926 Btu in ft−2 s−1
°F−1

=
6.933 Btu in ft−2 h−1
°F−1

=
0.577 8 Btu ft ft−2 h−1
°F−1

=
0.000 160 5 Btu ft ft−2s−1
°F−1

More extensive collections of thermal conductivity data
will be found in Touloukian et al. (1970a, b and c).

Thermal conductivities
of metallic elements

The thermal conductivity values in the
table below are for metallic elements in the purest polycrystalline condition
for which reliable measurements have been reported. Entries in italics relate
to the liquid phase.

The thermal conductivities of less pure samples of these elements will
be lower than the values given below. Thermal conductivity invariably decreases
with decreasing purity; such dependence being weak at ambient and higher
temperatures but very strong at cryogenic temperatures.

λ/(W
m−1 K−1)

Metal

Temperature/K

173.2

273.2

373.2

573.2

973.2

Aluminium

241

236

240

233

92

Antimony

33

25.5

22

19

27

Beryllium

367

218

168

129

93

Bismuth

11

8.2

7.2

13

17

Cadmium

100

97

95

89

45

Caesium

37

36

20

20.6

17.7

Cerium

8

11

13

16

—

Chromium

120

96.5

92

82

66

Cobalt

130

105

89

69

53

Copper

420

403

395

381

354

Dysprosium

9

10.5

—

—

—

Erbium

14

15

—

—

—

Gadolinium

12

10

—

—

—

Gallium†

43

41

33

45

—

Gold

324

319

313

299

272

Hafnium

25

23

22

21

21

Holmium

14

16

17

—

—

Indium

92

84

76

42

—

Iridium

156

147

145

139

—

Iron

99

83.5

72

56

34

Lanthanum

12

13

14.5

—

—

Lead

37

36

34

32

21

Lithium

94

86

82

47

59

Lutetium

18

17

—

—

—

Magnesium

160

157

154

150

—

Manganese

7

8

—

—

—

Mercury

29.5

7.8

9.4

11.7

—

Molybdenum

145

139

135

127

113

Nickel

113

94

83

67

71

Niobium

53

53

55

58

64

Osmium

93

88

87

87

—

Palladium

72

72

73

79

93

Platinum

73

72

72

73

78

Plutonium

4

6

8

—

—

Potassium

105

104

53

45

32

Praseodymium

9.9

12

13.4

—

—

Rhenium

52

49

47

44

45

Rhodium

156

151

147

137

—

Rubidium

59

58

32

29

22

Ruthenium

123

117

115

108

98

Samarium

10

13

13

14

—

Scandium

15

16

—

—

—

Silver

432

428

422

407

377

Sodium

141

142

88

78

60

Tantalum

58

57

58

58.5

60

Technetium

—

51

50

50

—

Terbium

11

10.5

—

—

—

Thallium

51

47

44

—

—

Thorium

55

54

54

56

58

Thulium

16

17

—

—

—

Tin

76

68

63

32

40

Titanium

26

22

21

19

21

Tungsten

188

177

163

139

119

Uranium

24

27

29

33

43

Vanadium

32

31

31

33

38

Yttrium

16.5

17

—

—

—

Zinc

117

117

112

104

66

Zirconium

26

23

22

21

23

† Values
for the a-axis which approximate to the polycrystal; those for the
b-axis are 91 and 88 and for the c-axis are 16.5 and 16 at
173.2 and 273.2 K.

Thermal conductivities of single crystals of
some non-cubic metals at normal temperature

λ/(W m−1
K−1)

Metal

Thermal conductivity in direction of

c-axis

a-axis

b-axis

Bismuth

5.4

9.3

Cadmium

83.05

104

Dysprosium

11.65

10.25

Erbium

18.4

12.6

Gadolinium

10.7

10.3

Gallium

16.0

40.8

88.3

Holmium

22.1

13.6

Lutetium

23.3

13.8

Mercury (at 227.7 K)

33.0

25.9

Terbium

14.5

9.45

Thulium

24.2

14.1

Tin

51.8

74.0

Thermal conductivities of
alloys

At low temperatures the thermal conductivity of a given metal tends to
increase in proportion to the reciprocal of its residual resistivity
ρ0. Many metals, especially good electrical conductors,
have thermal conductivities that follow the simple relation

λ =
L0σT

at very low temperatures and at
temperatures higher than their Debye temperature; L0 being
the Lorentz coefficient 2.45 × 10−8 W
s−1 K−2, σ the electrical
conductivity in S m−1 and T the absolute
temperature. This behaviour enables the thermal conductivities of metallic
samples to be estimated fairly reliably from simple electrical resistivity
measurements.

As the thermal conductivities of alloys depend strongly on their
mechanical and thermal history (heat treatment) as well as on their chemical
composition, the values tabulated below should be regarded as typical for the
compositions listed. For many groups of alloys the thermal conductivity of a
particular sample, near room temperature and above, can be estimated within
about 6% from its more easily
measured electrical conductivity using the relation λ = LσT
+ C. The optimum values for L and C for different alloy types are as
follows:

Main constituent metal

L/(10−8 W s −1
K−2)

C/(W m −1
K−1)

Aluminium . . . . . . . . . . . . . . . . . . . . . . . .

2.22

10.5

Copper . . . . . . . . . . . . . . . . . . . . . . . . .

2.39

7.5

Alpha-iron . . . . . . . . . . . . . . . . . . . . . . .

2.43

9.2

Gamma-iron . . . . . . . . . . . . . . . . . . . . . .

2.39

4.2

Magnesium . . . . . . . . . . . . . . . . . . . . . .

2.21

9.6

Nickel . . . . . . . . . . . . . . . . . . . . . . . . .

2.13

8.4

Nickel-chromium (nimonic type)
. . . . . . . . . . . .

2.20

6.0

Titanium . . . . . . . . . . . . . . . . . . . . . . . .

2.30

2.9

Zirconium . . . . . . . . . . . . . . . . . . . . . . .

2.50

2.2

For more detailed information on the
relationship between the thermal and electrical conductivities of alloys see:
Powell (1965), Hust and Clark (1971).

Composition and density may vary, values should be taken as typical of
type.

λ/(W m−1
K−1)

Material type

IEC classification

Temperature/K

298

373

773

1273

1773

Porcelains and clay-based

materials:

Siliceous

C-110, C-111

1.7–2.1

1.7–2.0

1.8–2.0

1.9–2.0

—

Steatite (normal)

C-220

5.5–6.0

—

2.8–3.7

—

—

Cordierite (dense)

C-410

1.5–2.5

1.5–2.5

—

—

—

Zircon (dense)

—

7

6

4

3.5

—

Clay-based refractories

C-512

2–3

2–3

2–3

2–3

—

Mullite

C-610

2–6

2–6

—

—

—

Oxides:

Alumina (>99.5%)†

C-799

33

29

12

9

7

Alumina 95%†

C-795

23

13

9

6

5

Alumina 90%†

C-786

17

12

7

5

4

Alumina 85%

C-780

15

12

7

4

—

Beryllia > 99.5%

C-810

300

220

70

18

14

Magnesia (30%
porous)†

C-820

10–14

5–8

—

—

—

Thoria (sintered)

—

8–10

6–8

3–5

2–3

—

Titania (sintered)

C-310

2.5–4

—

—

—

—

Urania (sintered)

—

8–10

6.8

4–5

2–3

2

Zirconia (stabilised)

C-830

1.7–2.0

1.7–2.0

1.7–2.0

1.7–2.2

1.8–3.3

† Values at high
temperatures are influenced by radiation transmission.

For further information on refractory materials consult
Morrell (1985). For further information on the thermal conductivities of
solid materials generally at high temperatures see, for example, Powell
(1954).

Thermal conductivities of miscellaneous
solids

The values below are for normal temperature, except
where stated (K) and should be regarded as average values for the type of
material specified. Values for the commoner polymers will be found in
section
3.11.1.

Thermal conductivities of some liquids and their
vapours (λ/(W
m−1 K−1))

In the table below the thermal
conductivities of liquids at their equilibrium saturation pressure are compared
with the values for their dilute vapours at the same temperatures.

He

H2

A

C6H6

H2O

KNO3

Temperature/K

4

20

90

298

373

683

Vapour

1.25 × 10−4

0.0145

0.0057

0.0070

0.0217

—

Liquid

0.0275

0.1178

0.1198

0.1463

0.6819

0.425

Thermal conductivities of gases

The thermal conductivity of a gas is
independent of pressure at normal pressures. It increases at high pressures and
decreases at low pressures, e.g. for air below about 1 mm Hg. Values are given
for a pressure of 1 atm.